Addition Law of Probability or Theorem of Total Probability
The probability that one of the several mutually exclusive events A1, A2,…., An will happen is the sum of the probabilities of the separate events. In symbols,
P (A1 + A2 + …..+ An) = P (A1)+P (A2) +… P(An) = ∑P(Ai).
Or
If an event can occur in any one of several mutually exclusive ways, the probability of that event is the sum of the individual probabilities of the different ways in which it can occur.
For example, when we toss a die, what is the probability of getting 2 or 4 or 6?
The probability of 2 = 1/6
The probability of 4 = 1/6
The probability of 6 = 1/6.
Therefore, probability of 2 or 4 or 6 is
1/6 + 1/6 + 1/6 = 3/6 = 1/2
